Calling a function an unspecified number of times

Question

I would like to be able to call a function an unspecified number of times. That is, I would like the generalization of something like:

   Sample[yi_, yf_, yinc_, zi_, zf_, zinc_]:=
          Table[{y, z}, {y, yi, yf, yinc}, {z, zi, zf, zinc}]

to $n$ variables, all with their own respective initial, finial and incremental values, and so I'd be calling on Table $n$ times. Is something like this even possible?

Answer 1

Something like :

sample[ranges_] := Table[Evaluate[ranges[[All, 1]]], Evaluate[Sequence @@ ranges]]

used like :

sample[{{x, 0, 3, 1}, {y, -2, 2, 1}}]

Answer 2

Going by the suggested syntax in your question you might find use in this:

sample[params__] := Range @@@ Partition[{params}, 3]

This does no type checking and assumes that your params list is in threes.
I kept it simple for ease of reading.

Example:

tbl = sample[3, 12, 2, 5, 1, -1]

{{3, 5, 7, 9, 11}, {5, 4, 3, 2, 1}}

On this output could use Outer:

Outer[ff, ##] & @@ tbl

{{ff[3, 5], ff[3, 4], ff[3, 3], ff[3, 2], ff[3, 1]},
 {ff[5, 5], ff[5, 4], ff[5, 3], ff[5, 2], ff[5, 1]},
 {ff[7, 5], ff[7, 4], ff[7, 3], ff[7, 2], ff[7, 1]},
 {ff[9, 5], ff[9, 4], ff[9, 3], ff[9, 2], ff[9, 1]},
 {ff[11, 5], ff[11, 4], ff[11, 3], ff[11, 2], ff[11, 1]}}

If you allow for more flexible syntax, you might use:

Outer[ff, ##] & @@ Range @@@ {{3, 12, 2}, {5, 1, -1}, {3}}